strongphysics - ch9

Chapter Nine - Circular Motion!

9.1 Rotation and Revolution

Rotation
- If an object rotates around a point continulously this is called rotation .
- An example of this would be the earth wich spins around its internal axis every day.
Revolution
- If an object rotates around an external axis this is called Revolution .
- An example of this is the earth rotating around the sun which acts as its external axis.

http://www.intelore.com/solar-system/solar-system-large.jpg

9.2 Rotational Speed

There are multiple ways of measuring roatational speed: linear, tangential, and angular speed.

Linear Speed
- The distance moved per unit of time.
- The linear speed is greater towards the edge of the rotating object because it is traveling more distance.
Angular Speed (!)
- Measures the amount of rotations which occur in a unit of time on a rigid body.
- Since it is measured on a rigid body all poits of the object are moving at the same rotational speed or RPM.
  - An example of this is a merry-go-round.

merrygoround.bmp

Tangential Speed (v)
- Measures how fast a single point on the object is moving when it is measured along a straight line tangent to the motion of that point.
  - The farther an object is from the axis the larger the tangential speed will be.
  - A point located on axis will have a tangential speed of zero.

Tangential speed and Angular speed are related through the equation: tangential speed = radial distance × angular speed or v = r!

9.3 Centripetal Force
Newton’s first law states that if an object is moving with no net force acting upon it then it will move in a straight line.

To continue the circular path of an object a constant force towards the center is required. This force is known as a centripetal (or center seekeng) force.

To find the centripital force (Fc) of an object of mass moving in a circle of radius (r) with a tangential speed (v) and angular speed (!) is found by the equation:

$\displaystyle _{\mathit{Fc}}=\frac{mv^2}{r}=mrw^2$

The corresponding centripetal acceleration ( ac) is...
$\displaystyle _{\math{ac}}=\frac{v^2}{r}=rw^2$

9.4 Centripetal and Centrifugal Forces
The force which causes the circular motion is a centripital force, not a centrifugal force.

Centrifugal force, which is a force acting outward, has no part in causing cirular motion.

9.5 Centrifugal Force in a Rotating Reference
If a person is in some object which is moving in a circular path it will seem to them that they are experiencing centrifugal force.

In actuality, centrifugal force does not exist. What you would be feeling is the reaction force to the object pushing you
toward the center of the circle.

No outward force (centrifugal force) exists on an object as a result of the object’s motion in a circle.

9.6 Simulated Gravity
If a space station were constructed in the shape of a large wheel such as the one pictured below, and the wheel was rotatingabout the axis, anyone on the inside of the wheel would feel that they were being pulled downward as if by gravity.
This is caused by the centripetal force which keeps the person moving in a circle, their reaction force will seem to pull them “down” but truely it is pushig them towards outside rim of the station.
The magnitude of the force acceleration or force experienced for the rotational speed is equally proportional to the radial distance to the floor or outer rim of the space station.

A larger space station would have a larger simulated gravity than a smaller one.
A smaller space station would also give a greater difference in apparent gravitational force from a person’s head to their feet than a larger one would.
- The smaller the space station, the less comfortable due to the difference in the gravitational force from head to toe.

Here is a non-rotational space station

Here is a diagram of a rotational space station

Physics 2008–2009 Mr. Strong
taken from:
https://www.mtlsd.org/Dashboard/Homework/homeworkfiles/huet87510xta/714385/arev09.pdf

ch9_cjlm